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(x^2y)^3: Understanding Exponent Rules
In algebra, exponent rules are essential to simplify and evaluate expressions. One common expression that requires the application of exponent rules is (x^2y)^3. In this article, we will explore how to simplify and evaluate this expression using the correct exponent rules.
What is the Exponent Rule?
The exponent rule, also known as the power rule, states that when an expression with an exponent is raised to another power, we multiply the exponents. Mathematically, it can be written as:
(a^m)^n = a^(mn)
Where a is the base, m and n are the exponents.
Simplifying (x^2y)^3
To simplify (x^2y)^3, we need to apply the exponent rule. Let's break it down step by step:
(x^2y)^3 = (x^2)^3 * y^3
Using the exponent rule, we multiply the exponents 2 and 3 to get:
(x^6) * y^3
So, the simplified form of (x^2y)^3 is x^6y^3.
Evaluating (x^2y)^3
To evaluate (x^2y)^3, we need to substitute values for x and y. Let's say x = 2 and y = 3. Then:
(2^2 * 3)^3 = (4 * 3)^3 = 12^3 = 1728
Therefore, the value of (x^2y)^3 when x = 2 and y = 3 is 1728.
Conclusion
In conclusion, simplifying and evaluating (x^2y)^3 requires the application of the exponent rule. By multiplying the exponents, we can simplify the expression to x^6y^3. Then, by substituting values for x and y, we can evaluate the expression to get its numerical value.
